It is well-known that the Poisson likelihood can be approximated as a quasi-Poisson regression model, see e.g. [1]}. For the adaptive lasso procedure, our theoretical contributions can also be seen as extension of work such as [2]} which provides asymptotic results for estimators from regularized generalized linear models. However, in our spatial framework, the more standard sample size must be substituted by, here, a mean number of points. Furthermore, observations are no more independent, i.e. our results are valid for a large class of spatial dependent point processes. Note also that [2]} assumes \(s_n=s\) .
